If x is the midpoint of line vy and wz
And the prove is triangle vwx is congruent triangle yzx can you help me solve this using two column prove
What would be the reasons for them
Sure! We can prove that triangle VWX is congruent to triangle YZX using a two-column proof. Here's a step-by-step guide on how to solve it:
Step 1: Given information
Start by stating the given information: "Given: X is the midpoint of line VY and WZ."
Step 2: Midpoint property
Using the midpoint property, we can state that "X divides VY and WZ into congruent segments." This is because a midpoint divides a line segment into two congruent segments.
Step 3: Definition of congruence
Next, use the definition of congruence: "Definition of Congruence: If two line segments have the same length, they are congruent."
Step 4: Segment VW congruent to segment YZ
Since X is the midpoint of VY and WZ, we can conclude that segment VW is congruent to segment YZ. This is because VY and WZ are divided into two congruent segments by X.
Step 5: Segment WX congruent to segment ZY
Similarly, we can conclude that segment WX is congruent to segment ZY. This is because X is the midpoint of VY and WZ, and each segment is divided into two congruent parts.
Step 6: Definition of congruent segments
Using the definition of congruent segments, we can write, "WX is congruent to ZY."
Step 7: Triangle VWX congruent to triangle YZX
Finally, using the Side-Side-Side (SSS) congruence criterion, we can state that "Triangle VWX is congruent to Triangle YZX." This is because we have established that all three pairs of corresponding sides are congruent (VW ≅ YZ, WX ≅ ZY, and VX ≅ YX).
And that completes the two-column proof!
since x is the midpoint,
wx = xz
vx = xy
<wxv = <yxz
by SAS, the triangles are congruent.